I’m interested in various topics in arithmetic geometry, like ranks of elliptic curves over function fields, curves over finite fields, Jacobian varieties and Galois representations.

Publications

  1. Vanishing of Hyperelliptic L-Functions at the Central Point, J. Number Theory 191 (2018), 85-103.
  2. Effective Bounds on the Dimensions of Jacobians Covering Abelian Varieties (Joint with Juliette Bruce), Proc. Amer. Math. Soc. 148 (2020), no. 2, 535-551
  3. Newton polygons of cyclic covers of the projective line branched at three points (Joint with Elena Mantovan, Rachel Pries, Yunqing Tang), Research Directions in Number Theory: Women in Numbers IV.
  4. Newton Polygons Arising for Special Families of Cyclic Covers of the Projective Line (Joint with Elena Mantovan, Rachel Pries, Yunqing Tang), Res. Number Theory 5 (2019), no. 1
  5. Ranks, 2-Selmer groups, and Tamagawa numbers of elliptic curves with Z/2ZxZ/8Z-torsion (Joint with Stephanie Chan, Jeroen Hanselman), ANTS XIII
  6. Newton Polygon Stratification of the Torelli Locus in PEL-type Shimura Varieties (Joint with Elena Mantovan, Rachel Pries, Yunqing Tang), to appear in IMRN
  7. Nonvanishing of hyperelliptic zeta functions over finite fields (Joint with Jordan Ellenberg, Mark Shusterman), Algebra Number Theory 14 (2020), no. 7, 1895-1909.
  8. Group-theoretic Johnson classes and a non-hyperelliptic curve with torsion Ceresa class (Joint with Dean Bisogno, Daniel Litt, Padmavathi Srinivasan), submitted
  9. The Ceresa class: tropical, topological, and algebraic (Joint with Daniel Corey, Jordan Ellenberg), submitted
  10. Surface bundles and the section conjecture (Joint with Daniel Litt, Nick Salter, Padmavathi Srinivasan), submitted
  11. Vanishing of Dirichlet L-functions at the central point over function fields (Joint with Ravi Donepudi), submitted
  12. Doubly isogenous genus-2 curves with D_4-action (Joint with Vishal Arul, Jeremy Booher, Steven R. Groen, Everett W. Howe, Vlad Matei, Rachel Pries, Caleb Springer), submitted
  13. Data for Shimura varieties intersecting the Torelli locus (Joint with Elena Mantovan, Rachel Pries)
  14. Abelian varieties of prescribed order over finite fields (Joint with Raymond van Bommel, Edgar Costa, Bjorn Poonen, Alexander Smith)

Slides and Poster

  1. Elliptic curves with rational Z2xZ8-torsion
  2. Poster
  3. Slides: Vanishing of Hyperelliptic L-Functions at the Central Point
  4. Slides: Effective Bounds on the Dimensions of Jacobians Covering Abelian Varieties